Set up the equation of the parabola in the given coordinate system between points C and B | Mathematics | Page 1

swift prawnBOT Oct 11, 2024, 10:25 AM

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keen kelp Oct 11, 2024, 10:34 AM

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So our parabola has the form ax^2

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When the parabola has a height of 13 on the positive side, it has a derivative of tan(90-67.8)=0.41

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Form a system of equations from this

pure furnace Oct 11, 2024, 10:40 AM

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Oh okay

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i'll try with this

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@keen kelp Can u help me find the coordinates for C?

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i can use Tan(B)*c right?

keen kelp Oct 11, 2024, 10:44 AM

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I mean I assumed u take C as the origin

pure furnace Oct 11, 2024, 10:44 AM

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the origin is here no?

keen kelp Oct 11, 2024, 10:44 AM

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Welp mb then

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Gimme a sec

pure furnace Oct 11, 2024, 10:45 AM

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alr

keen kelp Oct 11, 2024, 10:46 AM

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Yea I think it's easier to find the coefficient of the parabola first along with the x value for the height of 13

pure furnace Oct 11, 2024, 10:47 AM

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Which one here is the right one lol

keen kelp Oct 11, 2024, 10:48 AM

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pure furnace Which one here is the right one lol

Is this the answer key

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So we take C as the origin first
then
2ax=0.41
ax^2=13
Then solve for a and x
Afterwards then the coordinates of point C is
:(-x,0)

pure furnace Oct 11, 2024, 10:49 AM

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Wym?

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Okay I'll try

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wait i need to make it in the shown coordinate system, so i cant set the origin to C

keen kelp Oct 11, 2024, 11:04 AM

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You set the origin to C initially to find a

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Then you can find the distance of C from B

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If you want to find use the actual coordinate system

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Find the derivative of $a(x-x_1)^2$

teal minnowBOT Oct 11, 2024, 11:13 AM

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denzio321

keen kelp Oct 11, 2024, 11:14 AM

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Where x_1 is the unknown x coordinate of C

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Where g(x)=a(x-x_1)^2

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Then form the system of equations

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g(0)=13

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And g'(0)=tan(90-67.8)=0.41

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To solve for x_1 and a

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@pure furnace

#Set up the equation of the parabola in the given coordinate system between points C and B